Data adaptive ramp in a digital filter

ABSTRACT

A system and method for improving the performance of digital filters is disclosed. The data bandwidth and spectral control are improved by adaptively selecting ramp-up and ramp-down symbols based on the actual filtered data. Thus, the energy in the truncated tail of the filter is minimized for a given filter design. The invention is of particular utility in systems that filters intermittent data streams, thus requiring the filter to energize and deenergize repeatedly.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to digital systems. Morespecifically, the present invention relates to digital filters used tocontrol bandwidth in a communication system.

[0003] 2. Description of the Related Art

[0004] Modern communication systems have evolved from usingpredominantly analog circuitry to predominantly digital circuitry overthe past several years. Where there use to be passive and active analogcircuits used to oscillate, mix, filter and amplify signals in ‘analog’domain, there are now digital signal processing circuits that employspecialized microprocessors, DSP's and related circuits to processsignals in the digital domain. At the circuit component level, digitalcircuits are much more complex, employing millions of devices in somecircumstances. However, at the device level, digital communicationscircuits are much simpler, often times using just a handful of devicesto accomplish a complex communications task. Portable wireless devicesare good examples of this high level of integration. Digitalcommunications circuits also provide the substantial benefit ofprogrammability. A single device can serve many functions over time,allowing the system designer to closely tailor the function of thecommunications system to the needs of the effort at hand.

[0005] One particular functional area that has benefited from thetransition to the digital domain is signal filtering. As system designshave become more stringent, with narrowing bandwidths and higherinformation rates, analog filter topologies had become very complex,expensive, and prone to parts and circuit tolerance limitations. Analogfilters become rather poor choices when narrow bands, closechannelization, and high information rates force the need for very highorder filters to meet system design criteria. Fortunately, the advent ofdigital signal processing and digital filter theory has alleviated thisproblem to a great degree. However, digital filters are not withouttheir own limitations, and the state of the art has evolved to the pointwhere even digital filter designs are challenged to meet tight systemrequirement.

[0006] A particular family of filters that is commonly employed indigital communication systems implemented with digital filteringtechnology is the finite impulse response, or ‘FIR’, filter. Thesefilters are often characterized by linear phase response and constantgroup delay without feedback. In a typical implementation, a FIR filterresponse is implemented as a number of taps in a time domain delay line,each tap having an associated coefficient that defines the filterresponse characteristics. The number of taps indicates the order of thefilter, as well as the amount of processor overhead that is required toimplement the filter. The implementation of a FIR filter in a digitalsignal processor is widely understood by those skilled in the art. Infact, commercial software applications exist that allow designers toenter desired filter response parameters and then quickly produce filtertap coefficients that meet the design characteristics. Digital signalprocessing devices offer low level instructions designed to make filterimplementation as efficient as possible.

[0007] As is understood by those skilled in the art, digital filters,like any filter, can be represented in the frequency domain or the timedomain. In the frequency domain, segments of the filter transferfunction are delineated as the pass band, stop band and transition bandin a typical high-pass, low-pass, or band-pass filter. The frequencydomain can be readily transformed to the time domain. In the timedomain, the filter response is represented by an impulse function. Afilter designed in the frequency domain with a fixed frequency cutoffhas a theoretically infinite time impulse response to fully realize thecutoff frequency. Since time is always constrained, the impulse functionmust be truncated. However, truncating the time domain necessarilyresults in a broadening, or splattering, of energy bandwidth in thefrequency domain. Where a filter is used to control bandwidth, as inchannelizing a communications signal, this splattering of energy canresult in undesirable interference, noise, reduced system performance,and violation of FCC regulations. The problem is of particular concernin any system where the communications of information must be startedand stop with any regularity. A digital filter requires time to ramp upand produce useful output. Thus, there is a period of time at thebeginning and end of each transmission block of information which doesnot contribute to the communications of useful information through thesystem. In effect, the data throughput performance of the system iscompromised by the filter's limitations.

[0008] There are certain techniques available to those skilled in theart for controlling this limitation of digital filter systems. Onetechnique is to further truncate the filter at the beginning and ends oftransmission periods. This results in reduced system noise immunity andspectral spreading for those periods, but can be employed to advantagenone the less. Another technique is to reduce the ramp-up and ramp-downperiods for the filter and control the resultant spectral spreading bytruncating and windowing the data for the ramp periods. In effect, theenergy is forced to zero at the very beginning and ending moments of atime slot of signal transmission. Even given these techniques, thesystem designer is forced to exchange spectral efficiency for databandwidth performance in such systems. Thus, there is a need in the artto improve data throughput, by reducing ramp up and ramp down timeperformance in digital communication filters while maintaining controlof spectral performance.

SUMMARY OF THE INVENTION

[0009] The need in the art is addressed by the systems and methods ofthe present invention. An apparatus for reducing output energy andbandwidth of an intermittent data stream through a digital filter isdisclosed. The apparatus comprises a digital filter and a controllercoupled to the digital filter and operable to calculate at least a firstramp data field in accordance with coefficients selected to minimizeenergy in a truncated tail of the digital filter as a function of atleast a first data field. In a refinement of this apparatus, the firstdata field is adjacent to the ramp data field. In a further refinement,the controller is further operable to window the ramp data field. In afurther refinement, the controller is further operable to calculate bothof a ramp-up and a ramp-down ramp data field as a function of the atleast a first data field and a second data field respectively, and theramp-down coefficients are the mirror image of the ramp-up coefficients,provided that the digital filter is symmetrical.

[0010] Another apparatus is disclosed and serves the purpose ofgenerating coefficients (based on the digital filter tap weights) thatare used to calculate ramp symbols. The coefficients are derived byminimizing energy in the at least a first truncated tail data field as afunction of at least a first data field, and at least a first ramp datafield. At least a first coefficient is derived be setting the partialderivative of the energy of the at least a first truncated tail datafield with respect to at least a first ramp data field equal to zero,and solving the equation for the at least a first ramp data field. Thecoefficient of the at least a first data field in the solutionrepresents the at least a first coefficient in the solution for anarbitrary at least a first data filed. The present invention teaches andclaims a method for reducing the energy in the truncated tail of afilter response to a burst data by adaptively calculating ramp symbolsas a function of the data input to the digital filter.

[0011] A first method comprises the step of calculating at least a firstramp data field in accordance with coefficients selected to minimizeenergy in a truncated tail of the digital filter as a function of atleast a first data field. In a refinement of this method, the at least afirst data field is adjacent to the ramp data field. In anotherrefinement, the method also includes the step of windowing the ramp datafield. In a further refinement, the calculating step is applied to bothof a ramp-up and a ramp-down ramp data field as a function of the atleast a first information data field and a second information data fieldrespectively, and wherein ramp-down coefficients are the mirror image ofthe ramp-up coefficients.

[0012] Another method taught by the present invention comprises thesteps of calculating the energy in at least a first truncated tail datafield as a function of at least a first ramp data field variable and atleast a first data field variable, and taking a partial derivative ofthe energy in the at least a first truncated tail data field withrespect to the at least a first ramp data field variable. Then, writingan equality by setting the partial derivative equal to zero, and solvingthe equality for the at least a first ramp data field variable as afunction of the at least a first information data field therebygenerating at least a first coefficient. In a refinement of this method,the energy in the at least a first truncated tail data field is also afunction of the digital filter tap coefficients.

BRIEF DESCRIPTION OF THE DRAWINGS

[0013]FIG. 1 is a block diagram of a radio communications system used inan illustrative embodiment of the present invention.

[0014]FIG. 2 is a block diagram of a radio terminal unit used in anillustrative embodiment of the present invention.

[0015]FIG. 3 is a diagram of the radio spectrum utilized in anillustrative embodiment of the present invention.

[0016]FIG. 4 is a spectral diagram in an illustrative embodiment of thepresent invention.

[0017]FIG. 5 is a diagram of the TDMA data packet arrangement in anillustrative embodiment of the present invention.

[0018]FIG. 6 is a diagram a single TDM frame in an illustrativeembodiment of the present invention.

[0019]FIG. 7 is a functional block diagram of a transmitter/receiversystem in an illustrative embodiment of the present invention.

[0020]FIG. 8A is a diagram of the frequency responses curves of anillustrative embodiment digital filter.

[0021]FIG. 8B is a diagram of the time domain impulse response of anillustrative embodiment digital filter.

[0022]FIG. 9 is a diagram of the adaptive data ramp symbol packetstructure according to the present invention.

[0023]FIG. 10 is a diagram of a ramp-up window in a digital filter.

[0024]FIG. 11 is a diagram of a ramp-down window in a digital filter.

[0025]FIG. 12 is a diagram comparing the ramp-up response of a digitalfilter with and without windowing.

[0026]FIG. 13 is a frequency response diagram of a digital filtercomparing the ramp-up response with and without windowing.

[0027]FIG. 14 is a frequency response diagram of a digital filtercomparing the ramp-up response with and without adaptive ramping.

DESCRIPTION OF THE INVENTION

[0028] Illustrative embodiments and exemplary applications will now bedescribed with reference to the accompanying drawings to disclose theadvantageous teachings of the present invention. While the presentinvention is described herein with reference to illustrative embodimentsfor particular applications, it should be understood that the inventionis not limited thereto. Those having ordinary skill in the art andaccess to the teachings provided herein will recognize additionalmodifications, applications, and embodiments within the scope thereofand additional fields in which the present invention would be ofsignificant utility.

[0029] The preferred embodiment utilizes the present invention in atrunked land mobile radio system that employs FDM channelization andTDMA packetized data for channel trunking management, system control,data communications, and voice communications. Reference is directed toFIG. 1, which is a block diagram of such a system. The system includes arepeater base station 1 and a number of radio terminal units 4. The basestation 1 has a controller 2, which serves to control and interconnectseveral radio repeaters 6. In FIG. 1, three repeaters are shown,however, those skilled in the art understand that the number ofrepeaters is dependent upon the radio spectrum allocated to the systemand may range form one to twenty, or more, radio channels, and hence,one to twenty or more radio repeaters 6. In the United States, spectrumallocation is under the control of the Federal Communications Commission(FCC). The controller 2 provides various kinds of control of theresources in the base station 1, including interconnecting radio andwireline communications resources, and generating and interpretingcommunication protocols. The base station 1 includes radio frequencydistribution and combining circuits 8 which interconnect the severalradio repeaters 6 to one or more transmit/receive antennas 10.

[0030] The terminal units 4 communicate via radio frequency waves (notshown) with base station 1 via antenna 10. Reference is directed to FIG.2, which is a functional block diagram of a typical terminal unit 4. Inthe preferred embodiment, the terminal unit includes a controller 14interconnected to a radio transceiver 12, which couples through anantenna 11 to the base station 1. The terminal unit controller 14provides various control functions in the terminal unit includingmanaging the channel trunking operations, system control, datacommunications, and voice communication through the terminal unit 4. Thecontroller 14 also interfaces with a man-machine interface 16 (I/O) thatallows for user interaction with the terminal unit 4. The man-machineinterface includes audio input and output, user selectable functions,data input and output and so forth, as is understood by those skilled inthe art. The terminal unit also comprises a digital signal processingdevice 13 (hereinafter ‘DSP’) which is coupled to the controller 14, theman-machine interface 16, and the radio transceiver 12. Because theterminal unit 4 operates in multiple modes of operation, with a largenumber of system and user features, and according to a protocol withvarious utilizations of data communications, the DSP 13 greatlysimplifies the hardware design by providing for programmableflexibility. Of particular interest, with respect to the presentinvention, is the use of the DSP as a data filter to limit transmissionbandwidth in the terminal unit transmit mode.

[0031] In the preferred embodiment, the land mobile radio systemoperates in the US SMR band of frequencies that are allocated by theFCC. Reference is directed to FIG. 3, which is a spectral diagram 18 ofa typical spectrum allocation in the SMR band of frequencies. The US SMRband is defined as the ranges of frequencies from 806 MHz to 821 MHz andfrom 851 MHz and 866 MHz. Both ranges of frequencies are divided into 25kHz channels with the lower range of frequencies being referred to as‘reverse’ channels and the higher range of frequencies as ‘forward’channels. Forward channels being utilized for transmission from the basestation to the terminal units and reverse channels for transmissionsfrom terminal units to base stations. Following the three channelexample used above, the spectrum 18 has three reverse channels 20, whichare typically assigned at one megahertz intervals, in the range offrequencies from 806 MHz to 821 MHz, and, three forward channels 22 inthe range of frequencies from 851 MHz to 866 MHz. The channels arepaired, one forward channel with one reverse channel, and offset fromone another by 45 MHz. It is understood that any suitable band offrequencies would be usable in the preferred embodiment, such as the VHFband, the UHF band, or any other radio band.

[0032] In the preferred embodiment, the allocated channels areadvantageously sub-divided to improve capacity as is illustrated in FIG.4. Each of the reverse radio channel bands 20 (and each of the forwardchannel bands 22) centered about frequency F0 are subdivided with foursub-bands 25, 27, 29, and 31. Sub-band 29 is offset from the centerfrequency F0 by 2.4 kHz, sub-band 27 is offset from the center frequencyF0 by −2.4 kHz, sub-band 31 is offset from the center frequency F0 by7.2 kHz, and sub-band 25 is offset from the center frequency F0 by −7.2kHz. Each of the sub-carriers is independently modulated andindependently utilized as a communications resource. Since each sub-bandis further subdivided into two independent times slots, up to eightterminal units may occupy each allocated radio channel because each willreceive and transmit within one-half of the four sub-bands. For a morethorough description of the channelization scheme, attention is directedto co-pending U.S. patent application Ser. No. 09/295,660 filed Apr. 12,1999 entitled BANDWIDTH EFFICIENT QAM ON A TDM-FDM SYSTEM FOR WIRELESSCOMMUNICATIONS, assigned to the same assignee as the present invention,the contents of which is hereby incorporated by reference thereto.

[0033] It should be noted in FIG. 4 that the band allocation 22 of thereverse band and its transmission mask are defined by FCC regulationswithin Title 47 of the Code of Federal Regulations. Thus, anytransmitting terminal unit must control its transmission bandwidth so asnot to exceed the allocated band and mask constraints. Additionally,since each allocated band 20 in the preferred embodiment is furthersubdivided, each transmitting mobile must also control its modulation,or limit frequency splatter, so as not to interfere with other terminalunits transmitting on adjacent sub-bands. It will be appreciated bythose of ordinary skill in the art that the sub-band channelization inthe preferred embodiment defines a narrow-band system that challengesthe system designer in developing a robust product that does not causeundue inter-channel or inter-sub-band interference.

[0034] A further advantageous use of the radio spectrum within thepreferred embodiment is illustrated in FIG. 5. Each of the sub-carriersare digitally modulated and time division multiplexed to allow two, ormore, communications sessions to co-occupy the same radio frequencysub-band. One sub-channel of a forward channel 22 and the correspondingsub-channel of a reverse channel 20 are illustrated in FIG. 5. Eachcommunication session comprises a stream of data packets that aretransmitted on the appropriate channel and sub-channel as are defined bythe system protocol. The data transmitted includes channel trunking andcontrol data, data communications data, and digitized voice data, whichare all interleaved within the data packets. The two discrete TDMcommunication sessions are arbitrarily defined as the RED and BLUEsessions. In the preferred embodiment, the individual sessions arefurther segmented into a first and second TDM packet slot, thus in thecontinuous stream of data packets there are RED1, BLUE1, RED2 and BLUE2data slots. Therefore, as illustrated in FIG. 5, the forward channel 22comprises a stream of data slot packets transmitted by the base stationas RED1 24, BLUE1 26, RED2 28 and BLUE2 30, which repeat indefinitely.Similarly, the reverse channel 20 comprises a stream of data slotpackets transmitted by the terminal units as RED1 32, BLUE1 34, RED2 36and BLUE2 38, which also repeat indefinitely, so long as the terminalunits are transmitting. During idle periods, the reverse channels may bequiet, or just a fraction of the TDM slots may be occupied from time totime.

[0035] In operation, the terminal units, illustrated as block 4 in FIG.5, alternate between receiving a data slot packet on the forward channeland transmitting a data slot packet on the reverse channel. Forefficient terminal unit communications, the timing relationship betweenthe forward channel and reverse channel is staggered so that the forwardchannel RED packet slots align in time with the reverse channel BLUEpacket slots. So, when a terminal is assigned to the RED slot, then theterminal receives during the outbound RED slot and the terminaltransmits during the outbound BLUE slot. The transmit/receive switchingin the terminal units is thus efficiently managed.

[0036] Reference is directed to FIG. 6, which illustrates the data fieldcontent and general packet timing aspects of the terminal unit transmitpacket 40 according to the preferred embodiment of the presentinvention. The window duration for each of the aforementioned TDMA slotsaccording to the preferred embodiment of the present invention is thirtymilliseconds, 42 as illustrated in FIG. 6. Since the distance betweenthe terminal unit and the base station can range from nearly zero totwenty or more miles, it is necessary to factor in the propagation delayof the radio signals. This is accomplished by turning off the terminalunit transmitter before the end of the TDMA time window occurs, thusallowing time for the entire data content of each packet to propagatefrom the terminal unit to the base station receiver within the TDM slottime reference at the base station. In the preferred embodiment, thethirty millisecond TDMA window 42 is arbitrarily divided into onehundred twenty data field periods (250 microseconds each) which arenumbered from one to one hundred twenty. Thus, respecting thepropagation issue, the terminal unit is turned off during the last threedata field periods 44 in the preferred embodiment.

[0037] Turning off the transmitter for the last three data fieldsreduces the total number of transmitted data fields to one hundredseventeen 46. The first and last two of these fields, identified asitems 50, 52, 54, and 56, are used to ramp up and ramp down the digitalfilter to control spectral splattering, which concept will be more fullydeveloped hereinafter. Therefore, the data fields remaining fortransmission of usable data are one hundred twelve 48, as are indicatedby data field numbers three through one hundred fifteen in FIG. 6. Thecontent and use of the data symbols 48 are detailed in co-pending U.S.patent application Ser. No. 09/295,660 to West for BANDWIDTH EFFICIENTQAM ON A TDM-FDM SYSTEM FOR WIRELESS COMMUNNICATIONS.

[0038] The preferred embodiment utilizes a sixteen-point constellationquadrature amplitude modulation scheme (hereinafter ‘QAM’) for theencoding of data onto the radio frequency carrier. Therefore, each pointon the constellation defines one of sixteen data values, which aremapped to four-bit data fields, generally called 'symbols' by thoseskilled in the art. In FIG. 6, each of the data fields is used totransmit a single symbol, so the terms ‘data field’ and ‘symbol’ can beused interchangeably respecting the preferred embodiment, and otherimplementations of the present invention.

[0039] Reference is directed to FIG. 7, which is a functional blockdiagram of a transmitter circuit 58 and a receiver circuit 60 coupledtogether with a communications channel 92, according to an illustrativeembodiment of the present invention. In the transmitter circuit 58,either digitally sourced data 64 or analog sourced information 62, suchas audio signals, are coupled into the transmitter. Analog information62 is first filtered by low pass filter 66 to limit its bandwidth. Thefiltered signal is then digitized by analog to digital converter 68. Thedigitized analog signal is then coupled with digitally sourcedinformation 64 into mapping circuit 70. The concepts involved in pulsetiming, bit organization, and mapping of digital signals into theconstellation of a QAM modulator are well understood by those skilled inthe art. For reference, however, attention is directed to W. T. Webb andL. Hanzo, Modern Quadrature Amplitude Modulation, IEEE Press, 1994,chapter 3, pp. 80-93, the contents of which are hereby incorporated byreference thereto.

[0040] Mapping circuit 70 produces two digital outputs for the in-phaseand quadrature-phase inputs of the QAM modulator 76, which are coupledto a pair of Nyquist filters 72 and 74. The Nyquist filters areimplemented as 65-tap finite impulse response (hereinafter ‘FIR’)filters in a DSP in the preferred embodiment. Actually, since a Nyquistfilter impulse response is used to reduce inter-symbol interference atthe output of the modulator 76, the filters 72 and 74 generate asquare-root Nyquist response output, accomplished mathematically in theDSP. In preparation to modulation in the analog domain, the digitalsignals output by the square-root Nyquist filters 72 and 74 areconverted to the analog domain by digital to analog converters 71 and 73respectively. These signals are multiplied in the modulator 76 toproduce the desired Nyquist filter response characteristics. Within themodulator 76 is an intermediate frequency (hereinafter ‘IF’) referenceoscillator 78 that drives a first mixer 82. The filtered signal fromNyquist filter 72 is thus mixed with the IF in mixer 82. The IFoscillator 78 is also coupled though a 90° phase shift circuit 80, whichin turn couples to the second mixer 84. The output of the second Nyquistfilter 74 is mixed with the phase-shifted IF signal in mixer 84. The twomodulated IF signals are combined in adder 86 and output as a QAMmodulated IF signal from modulator 76. Finally, the QAM modulated IFsignal is mixed with a signal from a radio frequency (hereinafter ‘RF’)oscillator 90 in mixer 88, which outputs the QAM modulated RF carrier.The RF carrier is coupled to the receiver circuit 60 via channel 92. Inthe preferred embodiment, the channel 92 is via radio wave propagation.

[0041] The receiver circuit 60 in FIG. 7 performs essentially thereverse functions of the transmitter circuit 58. The QAM modulated RFsignal is received from channel 92 and coupled to a mixer 94 that isexcited by a RF oscillator 96. The resultant QAM modulated IF signal iscoupled to I&Q demodulator 96 which serves to recover the IF phase 98and to produce corresponding in-phase and quadrature-phase outputs atthe baseband. These analog signals are coupled to analog to digitalconverters 99 and 101 which convert the signals to the digital domainprior to subsequent coupling to square-root Nyquist digital filters 100and 102 respectively. The outputs of Nyquist filters 100 and 102comprise the received digital symbols, which are coupled to demappingcircuit 104. The received symbols are demapped and output directly asdigital signals 112, or coupled though digital to analog converter 106and filtered by low pass filter 108 to an analog output 110.

[0042] The advantages of using Nyquist filters in digital communicationssystems are well understood by those of ordinary skill in the art. Withthe advent of digital signal processing technology, Nyquist filters arenow commonly implemented as digital filters written as softwareapplications for a DSP, ASIC, or FPGA. Many are implemented as multi-tapFIR filters, often times of the raised-cosine variety. Naturally, alongwith the advantages of DSP technology and digital filtering, there arecertain limitations to be managed as well.

[0043] Major objectives of the design of the baseband digital filtersystem are to choose the transmitting and receiving filters to minimizethe effects of noise, eliminate or minimize inter-symbol interferenceand to reduce stop band energy. Inter-symbol interference cantheoretically be eliminated by proper shaping of the impulse responsecharacteristics of the transmitted signal. See FIG. 8B for reference.This shaping can be accomplished by causing the pulse to have zeromagnitude at periodic intervals equal to the symbol/information rate(the Nyquist criteria). Thus, as each transmitted impulse is overlaid intime with those before and after, the impulse for each falls at times ofzero energy for the others.

[0044] Modern implementations of pulse shaping filters use a pair ofmatched filters, one in the transmitter and one in the receiver. Theconvolution of the transmit filter with the receive filter forms thecomplete pulse shaping filter. Inter-symbol interference is avoidedsince the combined filter impulse response reaches unity at a singlepoint and is zero periodically at every other information point (theNyquist symbol/information rate). The linear superposition of pulsesrepresenting a pulse train preserves bandwidth and information content.Linear superposition of band limited pulses remains band limited andsampling the combined filter at the information rate at the correctsampling poinnt recovers the information.

[0045] Zero crossings of the impulse response function of a Nyquistfilter occur at the information rate, except at the one, center,information bearing point. All Nyquist filters having the same stop bandare theoretically equally bandwidth limited if the time response isallowed to go to infinity. Realizable filters, however, are truncated intime since it is not possible to have infinitely long impulse responses.With respect to the preferred embodiment, where a TDMA technique isemployed, the time domain is even more limited in that the terminal unittransmit energy should be at zero at the beginning and end of each 30 mstransmit window. Truncation error in the time domain causes thetheoretical stop band achievable by a Nyquist filter to be violated, sothat out of band energy exists in excess of the stop band frequency. Awell designed Nyquist filter balances this trade-off efficiently givensystem design criteria and the general need to obtain the best possibledata performance of the system.

[0046] The most efficient filter is the “brick wall” filter illustratedin FIG. 8A, where α=0 114. The stop-band transition is tightly cut-offat −f_(N) 124 and f_(N) 122. While the bandwidth efficiency istheoretically greatest for a brick wall filter as time approachesinfinity, truncation error causes poor performance for practicable andrealizable approximations to the brick wall filter. One method ofproducing practical filters is to allow the stop band of Nyquistcompliant filters to exceed the bandwidth of the ideal brick wall filterand smoothly transition to the stop band. A class of such filters is theraised-cosine filter. In the frequency domain, the raised cosine filteris continuous in the stop band.

[0047] To produce a realizable filter, the ideal filter is approximatedby time delaying and truncating the infinite impulse response.Truncation, however, produces unintentional out of band energy in excessof the theoretical stop band. One goal that is achieved by the presentinvention is to minimize this undesirable out of band energy after thefilter is truncated.

[0048] Attention is directed to FIGS. 8A and 8B. A Nyquist filter has animpulse response with equidistant zero-crossing points to eliminateinter-symbol interference. Nyquist showed that any odd-symmetryfrequency domain extension characteristic about f_(N) 122 and −f_(N) 124yields an impulse response with a unity value at the correct signalinginstant and zero crossing at all other sampling instants. Theraised-cosine characteristic meets these criteria by fitting a quarterperiod of a frequency-domain cosine shaped curve to an ideal (brickwall) filter characteristic.

[0049] The parameter controlling bandwidth of the raised cosine Nyquistfilter is the roll-off factor α. The roll-off factor α is one (α=1) 118if the ideal low pass filter bandwidth is doubled, that is the stop bandgoes to zero at twice the bandwidth 2f_(N) 126 (and −2f_(N) 128) of anideal brick wall filter at f_(N). If α=0.5 116 a total bandwidth f1.5f_(N) (not shown) would result, and so on. The lower the value of theroll-off factor a, the more compact the spectrum becomes but the longertime it takes for the impulse response to decay to zero. FIG. 8illustrates three cases, namely when α=0 114, α=0.5 116, and α=1 118.

[0050] In the time domain, referencing FIG. 8B, the impulse response ofthe Nyquist filter is greatest at zero and crosses zero at every integermultiple (both positive and negative) of the symbol/information period‘T’. The energy in the tails is greatest where α=0, less when α=0.5, andeven less where α=1. These reductions in the tail energy levels areinversely proportional to the amount of out of band, or stop-bandenergy.

[0051] In the preferred embodiment, the Nyquist filter is implemented asa digital filter at a 65 times oversample rate. The truncation length iseight symbol periods long, or sixteen total symbol periods, giving thenumber of the number of taps as sixteen times sixty-five, or onethousand twenty-four total taps. The filter is implemented in polyphaseform, where the unique data inputs occur at the symbol rate. Polyphaseimplementation of digital filters is a well known digital technique tothe of ordinary skill in the at. Theoretical Nyquist filters are notrealizable (since infinite time in both directions is necessary to fullyrealize the theoretical stop band properties of the filter). PracticalNyquist filters are made by time delaying and truncating the infiniteimpulse response. After choosing the α factor, the oversample rate (65)and the number of symbol time delays for the filter to realize thesymbol value (8), fully specifies the filter tap values for the exampleraised cosine class of filters.

[0052] Given the digital filter design and the eight period decay time,out of band energy is naturally controlled to the filter'sdigital/truncation limit, according to the α factor selected in thedesign. However, since the filter operates in a TDMA system, it mustramp up and ramp down during every 30 ms TDM slot interval. In/a pulseshaping filter, the filter is normally initialized with zeros, and thenatural ramp up takes a delay of eight (in this instance) symbols torealize the first information point. The natural ramp down also takeseight zeros (at the sampling rate) to ramp the filter down in aspectrally efficient way. Sacrificing eight leading and eight trailingsymbol periods in a 120 symbol slot interval to control bandwidth isundesirably wasteful of system and information data bandwidth. One wayto improve the efficiency of the design is to truncate the eight symbolperiods to a lesser number of symbol periods at the beginning and end ofa slot. In the preferred embodiment, the ramp times are truncated to twosymbol periods for both the ramp-up and ramp-down periods. The effect oftruncating these periods is to generate out of band spectral energysplatter. The present invention reduces this splatter while preservingthe data bandwidth efficiency.

[0053] The assignee of the present invention has already filed aco-pending patent application for an improved Nyquist filter design. Theapplication is Ser. No. 09/307,078 and entitled IMPROVED NYQUIST FILTERAND METHOD, which was filed in the US Patent Office on Apr. 28, 1999,the contents of which are hereby incorporated by reference thereto.

[0054] Reference is directed to FIG. 9, which is a data timing diagramof a single TDMA data slot in the preferred embodiment of the presentinvention. The transmitted symbols 130 comprise symbols one through onehundred seventeen. Symbols one 134 and two 136 are used to ramp-up thedigital filter in the time domain. Symbols one hundred sixteen 140 andone hundred seventeen 138 are used to ramp down the digital filter inthe time domain (the other natural ramp symbols having been truncated bydesign). Note that these symbols are generally described as the rampsymbols. The present invention teaches and claims an apparatus andmethod of generating ramp data values that reduce energy in thetruncated tail of a digital filter.

[0055] The preferred embodiment digital filter operates on four-bitsymbols with an over sampling rate of sixty-five times. A modifiedNyquist filter is employed and the time domain impulse curve is suchthat eight data symbols is sufficient to provide adequate guard bandsplatter control. However, for protocol efficiency, the prior art filterutilizes two zero-valued ramp-up and ramp-down data fields withwindowing to more quickly ramp the filter and allow for twelveadditional useful data symbol periods.

[0056] The truncated ramp-up tail 142 is comprised of data symbols Q1,Q2, Q3, Q4, Q5, Q6, Q7, and Q8. Similarly, the truncated ramp-down tail144 comprises symbols Q8, Q7, Q6, Q5, Q4, Q3, Q2, and Q1. The rampsymbols do not carry useful data. In the present invention, the firstsix data symbols 148 and the last six data symbols 150 (identified assymbols S3, S4, S5, S6, S7, and S8 in FIG. 9) are used to calculateadaptive ramp symbol values designed to reduce the energy level in thetruncated tail portions 142 and 144 to a minimun so that out of bandenergy splatter is minimized. In the prior art, a windowing approach wasused to reduce the energy in the truncated tail. An exponential functionwas used (among other functions, as are understood by those of ordinaryskill in the art) to quickly ramp the filter while minimizing the energyin the truncated tails. While this approach is beneficial, it is a fixedscheme and operates independent of the actual data present in thesubsequent bit stream 150 and preceding bit steam 148. Since the datapresent in the bit streams 148 and 150 have an impact on the truncatedtail portion of the digital filter, the energy content of the truncatedtail even with windowing applied, cannot operate at an optimum.

[0057]FIG. 10 shows the ramp-up windowing function magnitude curve 154as a function of sample points for the first two transmitted data symbolperiods. FIG. 11 shows the ramp-down windowing function magnitude curve158 as a function of sample numbers for the last two transmitted symbolperiods. As mentioned above, the prior art windowing function is anexponential function. FIG. 12 shows a comparison of the signal amplitudefor an exemplary data stream with and without the windowing functionapplied to the two-symbol ramp. It can be seen that the frequencyamplitude is more efficient in the far stop band in the windowed curve164 as opposed to the non-windowed curve 162. The benefits of this areclearly visible in FIG. 13, which depicts the spectrum amplituderesponse 166 as a function of frequency for both the windowed andnon-windowed ramp. The pass band response for the two visiblesub-channels 167 and 169 show that the filters operate the same in thepass band. In the stop band, the windowed curve 170, with zero rampsymbols, shows a significant improvement in rejection performance (about10 dB). However, in the transitional area indicated by region 172 inFIG. 13, it can be seen that the windowed ramp actually under performsthe non-windowed ramp. As will be appreciated by those skilled in theart, the transitional area is of great importance in system designbecause it is this region that typically encroaches on the mandatedspectral envelope.

[0058] The present invention improves upon not only the non-windowedramp, but the windowed ramp as well, by adapting the ramp symbol valuesto the transmitted symbol data. The energy in the truncated tail can beminimized and spectral splatter attenuated. A descriptive andmathematical analysis of this approach follows. Reference is directedagain to FIG. 9 for an understanding of where the various symbol periodsfall in time with respect to one another. The following analysis is withrespect to the ramp-up ramp, however, those of ordinary skill in the artwill appreciate that the ramp-down ramp is merely a mirror image of theramp-up ramp, and hence the analysis is complete for both ramps;however, the design can be easily extended to filters withnon-symmetrical, or complex response.

[0059] In the preferred embodiment, the total energy in the tail can bewritten using the first eight symbols periods (and last eight symbolperiods). Of course, in other filter designs, the number of periods mayvary as well as the over sampling rate, as is understood by those ofordinary skill in the art. At 65 times over sampling, the magnitudes ofeach sample point in the truncated tail portion 142 is contained in oneof the following vectors, (where Q_(x) is the symbol period of datapoints, R_(x) (or S_(x)) is the symbol value of the correspondingtransmitted data, and h_(y) is the filter tap, or coefficient, value.

[0060] The first truncated symbol period sample data output isdetermined by the first 65 data sample points: $\begin{matrix}{{\overset{\rightharpoonup}{Q}}_{1} = \begin{Bmatrix}{h_{0}R_{1}} \\{h_{1}R_{1}} \\\vdots \\{h_{64}R_{1}}\end{Bmatrix}} & {{Eq}.\quad 1}\end{matrix}$

[0061] The second truncated symbol period sample data output isdetermined by the next 65 data sample points: $\begin{matrix}{{\overset{\rightharpoonup}{Q}}_{2} = \begin{Bmatrix}{{h_{65}R_{1}} + {h_{0}R_{2}}} \\{{h_{66}R_{1}} + {h_{1}R_{2}}} \\\vdots \\{{h_{129}R_{1}} + {h_{64}R_{2}}}\end{Bmatrix}} & {{Eq}.\quad 2}\end{matrix}$

[0062] The third truncated symbol period sample data output isdetermined by the third 65 data sample points: $\begin{matrix}{{\overset{\rightharpoonup}{Q}}_{3} = \begin{Bmatrix}{{h_{130}R_{1}} + {h_{65}R_{2}} + {h_{0}S_{3}}} \\{{h_{131}R_{1}} + {h_{66}R_{2}} + {h_{1}S_{3}}} \\\vdots \\{{h_{194}R_{1}} + {h_{129}R_{2}} + {h_{64}S_{3}}}\end{Bmatrix}} & {{Eq}.\quad 3}\end{matrix}$

[0063] The fourth truncated symbol period sample data output isdetermined by the fourth 65 data sample points: $\begin{matrix}{{\overset{\rightharpoonup}{Q}}_{4} = \begin{Bmatrix}{{h_{195}R_{1}} + {h_{130}R_{2}} + {h_{65}S_{3}} + {h_{0}S_{4}}} \\{{h_{196}R_{1}} + {h_{131}R_{2}} + {h_{66}S_{3}} + {h_{1}S_{4}}} \\\vdots \\{{h_{259}R_{1}} + {h_{194}R_{2}} + {h_{129}S_{3}} + {h_{64}S_{4}}}\end{Bmatrix}} & {{Eq}.\quad 4}\end{matrix}$

[0064] The fifth truncated symbol period sample data output isdetermined by the fifth 65 data sample points: $\begin{matrix}{{\overset{\rightharpoonup}{Q}}_{5} = \begin{Bmatrix}{{h_{260}R_{1}} + {h_{195}R_{2}} + {h_{130}S_{3}} + {h_{65}S_{4}} + {h_{0}S_{5}}} \\{{h_{261}R_{1}} + {h_{196}R_{2}} + {h_{131}S_{3}} + {h_{66}S_{4}} + {h_{1}S_{5}}} \\\vdots \\{{h_{324}R_{1}} + {h_{259}R_{2}} + {h_{194}S_{3}} + {h_{129}S_{4}} + {h_{64}S_{5}}}\end{Bmatrix}} & {{Eq}.\quad 5}\end{matrix}$

[0065] The sixth truncated symbol period sample data output isdetermined by the sixth 65 data sample points: $\begin{matrix}{{\overset{\rightharpoonup}{Q}}_{6} = \begin{Bmatrix}{{{h_{325}R_{1}} + {h_{260}R_{2}} + {h_{195}S_{3}} + {h_{130}S_{4}} + {h_{65}S_{5}} +},{h_{0}S_{6}}} \\{{h_{326}R_{1}} + {h_{261}R_{2}} + {h_{196}S_{3}} + {h_{131}S_{4}} + {h_{66}S_{5}} + {h_{1}S_{6}}} \\\vdots \\{{{h_{389}R_{1}} + {h_{324}R_{2}} + {h_{259}S_{3}} + {h_{194}S_{4}} +},{{h_{129}S_{5}} + {h_{64}S_{6}}}}\end{Bmatrix}} & {{Eq}.\quad 6}\end{matrix}$

[0066] The seventh truncated symbol period sample data output isdetermined by the seventh 65 data sample points: $\begin{matrix}{{\overset{\rightharpoonup}{Q}}_{7} = \begin{Bmatrix}{{h_{390}R_{1}} + {h_{325}R_{2}} + {h_{269}S_{3}} + {h_{195}S_{4}} + {h_{130}S_{5}} + {h_{65}S_{6}} + {h_{0}S_{7}}} \\{{h_{391}R_{1}} + {h_{326}R_{2}} + {h_{270}S_{3}} + {h_{195}S_{4}} + {h_{131}S_{5}} + {h_{66}S_{6}} + {h_{1}S_{7}}} \\\vdots \\{{h_{454}R_{1}} + {h_{389}R_{2}} + {h_{324}S_{3}} + {h_{259}S_{4}} + {h_{194}S_{5}} + {h_{129}S_{6}} + {h_{64}S_{7}}}\end{Bmatrix}} & {{Eq}.\quad 7}\end{matrix}$

[0067] The eighth truncated symbol period sample data output isdetermined by the eighth 65 data sample points: $\begin{matrix}{{\overset{\rightharpoonup}{Q}}_{8} = \begin{Bmatrix}{{h_{455}R_{1}} + {h_{390}R_{2}} + {h_{325}S_{3}} + {h_{260}S_{4}} + {h_{195}S_{5}} + {h_{130}S_{6}} + {h_{64}S_{7}} + {h_{0}S_{8}}} \\{{h_{456}R_{1}} + {h_{391}R_{2}} + {h_{326}S_{3}} + {h_{261}S_{4}} + {h_{196}S_{5}} + {h_{131}S_{6}} + {h_{65}S_{7}} + {h_{1}S_{8}}} \\\vdots \\{{h_{519}R_{1}} + {h_{454}R_{2}} + {h_{389}S_{3}} + {h_{324}S_{4}} + {h_{259}S_{5}} + {h_{194}S_{6}} + {h_{129}S_{7}} + {h_{64}S_{8}}}\end{Bmatrix}} & {{Eq}.\quad 8}\end{matrix}$

[0068] The sum of the squares for each of the sixty-five sample pointsof the eight truncated symbol periods indicates the total energy in thetruncated tail, as follows: $\begin{matrix}{E = {\sum\limits_{i = 0}^{64}\left( {Q_{1_{i}}^{2} + Q_{2_{i}}^{2} + Q_{3_{i}}^{2} + Q_{4_{i}}^{2} + Q_{5_{i}}^{2} + Q_{6_{i}}^{2} + Q_{7_{i}}^{2} + Q_{8_{i}}^{2}} \right)}} & {{Eq}.\quad 9}\end{matrix}$

[0069] The ramp up symbol values are calculated by solving the leastsquares to minimize the amount of energy in the truncated tail symbols.The partial derivative of the energy with respect to the two rampsymbols are taken to accomplish this step, as follows: $\begin{matrix}{{{{{Respecting}\quad {Symbol}\quad {R_{1}:\frac{\partial E}{\partial R_{1}}}} = {\sum\limits_{i = 0}^{64}\left( {{2\frac{\partial Q_{1}}{\partial R_{1}}Q_{1_{i}}} + {2\frac{\partial Q_{2_{i}}}{\partial R_{1}}Q_{2_{i}}} + \ldots + {2\frac{\partial Q_{8_{i}}}{\partial R_{1}}Q_{8_{i}}}} \right)}}{and}}\quad} & {{Eq}.\quad 10} \\{{{Respecting}\quad {Symbol}\quad {R_{2}:\frac{\partial E}{\partial R_{2}}}} = {\sum\limits_{i = 0}^{64}\left( {{2\frac{\partial Q_{1_{i}}}{\partial R_{2}}Q_{1_{i}}} + {2\frac{\partial Q_{2_{i}}}{\partial R_{2}}Q_{2_{i}}} + \ldots + {2\frac{\partial Q_{8_{i}}}{\partial R_{2}}Q_{8_{i}}}} \right)}} & {{Eq}.\quad 11}\end{matrix}$

[0070] For clarity and simplicity, the individual terms contributing tothe energy in R₁ and R₂ in the above equations with respect to eachvector are individually expressed, and appear below for both R₁ and R₂for each term of Equations Eq. 10 and Eq. 11.

[0071] First term for Eq. 10 and Eq. 11 respectively: $\begin{matrix}{{{\sum\limits_{l = 0}^{64}\frac{\partial Q_{l_{i}}^{2}}{\partial R_{1}}} = {{2{\sum\limits_{l = 0}^{64}{\frac{\partial Q_{1_{i}}}{\partial R_{1}}Q_{1_{i}}}}} = {2\left( {\sum\limits_{l = 0}^{64}h_{l}^{2}} \right)R_{1}}}}{and}} & {{Eq}.\quad 12} \\{{\sum\limits_{l = 0}^{64}{\frac{\partial Q_{1_{i}}}{\partial R_{2}}Q_{1_{i}}}} = 0} & {{Eq}.\quad 13}\end{matrix}$

[0072] as there is no R₂ argument in the first term.

[0073] Second term for Eq. 10 and Eq. 11 respectively: $\begin{matrix}{{{2{\frac{\partial{\overset{\rightharpoonup}{Q}}_{2}}{\partial R_{1}} \cdot {\overset{\rightharpoonup}{Q}}_{2}}} = {2\left\{ {{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 65} \right)\left( h_{l} \right)}} \right\rbrack R_{2}} + {\left\lbrack {\sum\limits_{l = 0}^{64}\left( h_{l + 65} \right)^{2}} \right\rbrack R_{1}}} \right\}}}\quad {and}} & {{Eq}{.14}} \\{{2{\frac{\partial{\overset{\rightharpoonup}{Q}}_{2}}{\partial R_{2}} \cdot {\overset{\rightharpoonup}{Q}}_{2}}} = {2\left\{ {{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 65} \right)\left( h_{l} \right)}} \right\rbrack R_{1}} + {\left\lbrack {\sum\limits_{l = 0}^{64}h_{l}^{2}} \right\rbrack R_{2}}} \right\}}} & {{Eq}.\quad 15}\end{matrix}$

[0074] Third term for Eq. 10 and Eq. 11 respectively: $\begin{matrix}{{{2{\frac{\partial{\overset{\rightharpoonup}{Q}}_{3}}{\partial R_{1}} \cdot {\overset{\rightharpoonup}{Q}}_{3}}} = {2\left\{ {{\left\lbrack {\sum\limits_{l = 0}^{64}h_{l + 130}^{2}} \right\rbrack R_{1}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 65} \right)\left( h_{l + 130} \right)}} \right\rbrack R_{2}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 130} \right)\left( h_{l} \right)}} \right\rbrack S_{3}}} \right\}}}{and}} & {{Eq}.\quad 16} \\{{2{\frac{\partial{\overset{\rightharpoonup}{Q}}_{3}}{\partial R_{2}} \cdot {\overset{\rightharpoonup}{Q}}_{3}}} = {2\left\{ {{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 130} \right)\left( h_{l + 65} \right)}} \right\rbrack R_{1}} + {\left\lbrack {\sum\limits_{l = 0}^{64}h_{l + 65}^{2}} \right\rbrack R_{2}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 65} \right)\left( h_{l} \right)}} \right\rbrack S_{3}}} \right\}}} & {{Eq}.\quad 17}\end{matrix}$

[0075] Fourth term for Eq. 10 and Eq. 11 respectively: $\begin{matrix}{{{2{\frac{\partial{\overset{\rightharpoonup}{Q}}_{4}}{\partial R_{1}} \cdot {\overset{\rightharpoonup}{Q}}_{4}}} = {2\begin{Bmatrix}{{\left\lbrack {\sum\limits_{l = 0}^{64}h_{l + 195}^{2}} \right\rbrack R_{1}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 195} \right)\left( h_{l + 130} \right)}} \right\rbrack R_{2}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 195} \right)\left( h_{l + 65} \right)}} \right\rbrack S_{3}} +} \\{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l} \right)\left( h_{l + 195} \right)}} \right\rbrack S_{4}}\end{Bmatrix}}}{and}} & {{Eq}.\quad 18} \\{{2{\frac{\partial{\overset{\rightharpoonup}{Q}}_{4}}{\partial R_{2}} \cdot {\overset{\rightharpoonup}{Q}}_{4}}} = {2\begin{Bmatrix}{\quad {{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 195} \right)\left( h_{l + 130} \right)}} \right\rbrack R_{1}} + {\left\lbrack {\sum\limits_{l = 0}^{64}h_{l + 130}^{2}} \right\rbrack R_{2}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 130} \right)\left( h_{l + 65} \right)}} \right\rbrack S_{3}} +}} \\{\quad {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 130} \right)\left( h_{l} \right)}} \right\rbrack S_{4}}}\end{Bmatrix}}} & {{Eq}.\quad 19}\end{matrix}$

[0076] Fifth term for Eq. 10 and Eq. 11 respectively: $\begin{matrix}{{{2{\frac{\partial{\overset{\rightharpoonup}{Q}}_{5}}{\partial R_{1}} \cdot {\overset{\rightharpoonup}{Q}}_{5}}} = {2\begin{Bmatrix}{\quad {{\left\lbrack {\sum\limits_{l = 0}^{64}h_{l + 260}^{2}} \right\rbrack R_{1}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 260} \right)\left( h_{l + 195} \right)}} \right\rbrack R_{2}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 260} \right)\left( h_{l + 130} \right)}} \right\rbrack S_{3}} +}} \\{\quad {{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 260} \right)\left( h_{l + 65} \right)}} \right\rbrack S_{4}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 260} \right)\left( h_{l} \right)}} \right\rbrack S_{5}}}}\end{Bmatrix}}}{and}} & {{Eq}.\quad 20} \\{{2{\frac{\partial{\overset{\rightharpoonup}{Q}}_{5}}{\partial R_{2}} \cdot {\overset{\rightharpoonup}{Q}}_{5}}} = {2\begin{Bmatrix}{\quad {{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 260} \right)\left( h_{l + 195} \right)}} \right\rbrack R_{1}} + {\left\lbrack {\sum\limits_{l = 0}^{64}h_{l + 195}^{2}} \right\rbrack R_{2}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 195} \right)\left( h_{l + 130} \right)}} \right\rbrack S_{3}} +}} \\{\quad {{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 195} \right)\left( h_{l + 65} \right)}} \right\rbrack S_{4}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 195} \right)\left( h_{l} \right)}} \right\rbrack S_{5}}}}\end{Bmatrix}}} & {{Eq}.\quad 21}\end{matrix}$

[0077] Sixth term for Eq. 10 and Eq. 11 respectively:$\quad \begin{matrix}{{{2{\frac{\partial{\overset{\rightharpoonup}{Q}}_{6}}{\partial R_{1}} \cdot {\overset{\rightharpoonup}{Q}}_{6}}} = {2\begin{Bmatrix}{{\left\lbrack {\sum\limits_{l = 0}^{64}h_{l + 325}^{2}} \right\rbrack R_{1}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 325} \right)\left( h_{l + 260} \right)}} \right\rbrack R_{2}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 325} \right)\left( h_{l + 195} \right)}} \right\rbrack S_{3}} +} \\{{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 325} \right)\left( h_{l + 130} \right)}} \right\rbrack S_{4}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 325} \right)\left( h_{l + 65} \right)}} \right\rbrack S_{5}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 325} \right)\left( h_{l} \right)}} \right\rbrack S_{6}}}\end{Bmatrix}}}{and}} & {{Eq}.\quad 22} \\{{2{\frac{\partial{\overset{\rightharpoonup}{Q}}_{6}}{\partial R_{2}} \cdot {\overset{\rightharpoonup}{Q}}_{6}}} = {2\begin{Bmatrix}{{{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 325} \right)\left( h_{l + 260} \right)}} \right\rbrack R_{1}} + {\left\lbrack {\sum\limits_{l = 0}^{64}h_{l + 260}^{2}} \right\rbrack R_{2}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 260} \right)\left( h_{l + 195} \right)}} \right\rbrack S_{3}} +}\quad} \\{{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 260} \right)\left( h_{l + 130} \right)}} \right\rbrack S_{4}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 260} \right)\left( h_{l + 65} \right)}} \right\rbrack S_{5}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 260} \right)\left( h_{l} \right)}} \right\rbrack S_{6}}}\end{Bmatrix}}} & {{Eq}.\quad 23}\end{matrix}$

[0078] Seventh term for Eq. 10 and Eq. 11 respectively: $\begin{matrix}{\quad {{{2{\frac{\partial{\overset{\rightharpoonup}{Q}}_{7}}{\partial R_{1}} \cdot \overset{{\overset{\rightharpoonup}{\rightharpoonup}}_{7}}{S}}} = {2\begin{Bmatrix}{{\left\lbrack {\sum\limits_{l = 0}^{64}h_{l + 390}^{2}} \right\rbrack R_{1}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 390} \right)\left( h_{l + 325} \right)}} \right\rbrack R_{2}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 390} \right)\left( h_{l + 260} \right)}} \right\rbrack S_{3}} +} \\{{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 390} \right)\left( h_{l + 195} \right)}} \right\rbrack S_{4}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 390} \right)\left( h_{l + 130} \right)}} \right\rbrack S_{5}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 390} \right)\left( h_{l + 65} \right)}} \right\rbrack S_{6}} +} \\{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 390} \right)\left( h_{l} \right)}} \right\rbrack S_{7}}\end{Bmatrix}}}\text{}{and}}} & {{Eq}{.24}} \\{\quad {{2{\frac{\partial{\overset{\rightharpoonup}{Q}}_{7}}{\partial R_{2}} \cdot {\overset{\rightharpoonup}{Q}}_{7}}} = {2\begin{Bmatrix}{\quad {{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 390} \right)\left( h_{l + 325} \right)}} \right\rbrack R_{1}} + {\left\lbrack {\sum\limits_{l = 0}^{64}h_{l + 325}^{2}} \right\rbrack R_{2}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 325} \right)\left( h_{l + 260} \right)}} \right\rbrack S_{3}} +}} \\{\quad {{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 325} \right)\left( h_{l + 195} \right)}} \right\rbrack S_{4}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 325} \right)\left( h_{l + 130} \right)}} \right\rbrack S_{5}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 325} \right)\left( h_{l + 65} \right)}} \right\rbrack S_{6}} +}} \\{\quad {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 325} \right)\left( h_{l} \right)}} \right\rbrack S_{7}}}\end{Bmatrix}}}} & {{Eq}.\quad 25}\end{matrix}$

[0079] Eighth term for Eq. 10 and Eq. 11 respectively: $\begin{matrix}{\quad {{{2{\frac{\partial{\overset{\rightharpoonup}{Q}}_{8}}{\partial R_{1}} \cdot {\overset{\rightharpoonup}{Q}}_{8}}} = {2\begin{Bmatrix}{{\left\lbrack {\sum\limits_{l = 0}^{64}h_{l + 455}^{2}} \right\rbrack R_{1}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 455} \right)\left( h_{l + 390} \right)}} \right\rbrack R_{2}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 455} \right)\left( h_{l + 325} \right)}} \right\rbrack S_{3}} +} \\{{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 455} \right)\left( h_{l + 260} \right)}} \right\rbrack S_{4}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 455} \right)\left( h_{l + 195} \right)}} \right\rbrack S_{5}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 455} \right)\left( h_{l + 130} \right)}} \right\rbrack S_{6}} +} \\{{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 455} \right)\left( h_{l + 65} \right)}} \right\rbrack S_{7}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 455} \right)\left( h_{l} \right)}} \right\rbrack S_{8}}}\end{Bmatrix}}}\text{}{and}}} & {{Eq}.\quad 26} \\{\quad {{2{\frac{\partial{\overset{\rightharpoonup}{Q}}_{8}}{\partial R_{2}} \cdot {\overset{\rightharpoonup}{Q}}_{8}}} = {2\begin{Bmatrix}{{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 455} \right)\left( h_{l + 390} \right)}} \right\rbrack R_{1}} + {\left\lbrack {\sum\limits_{l = 0}^{64}h_{l + 390}^{2}} \right\rbrack R_{2}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 390} \right)\left( h_{l + 325} \right)}} \right\rbrack S_{3}} +} \\{{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 390} \right)\left( h_{l + 260} \right)}} \right\rbrack S_{4}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 390} \right)\left( h_{l + 195} \right)}} \right\rbrack S_{5}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 390} \right)\left( h_{l + 130} \right)}} \right\rbrack S_{6}} +} \\{{\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 390} \right)\left( h_{l + 65} \right)}} \right\rbrack S_{7}} + {\left\lbrack {\sum\limits_{l = 0}^{64}{\left( h_{l + 390} \right)\left( h_{l} \right)}} \right\rbrack S_{8}}}\end{Bmatrix}}}} & {{Eq}.\quad 27}\end{matrix}$

[0080] The sum of all derivative terms is zero, giving two equations andtwo unknowns, for the least squares. The sample points are summed andorganized to yield the following: $\quad \begin{matrix}{\begin{matrix}{\quad {{\left( \quad {\sum\limits_{l = 0}^{519}h_{l}^{2}} \right)R_{1}} + {\left( {\sum\limits_{l = 0}^{454}{h_{l}h_{l + 65}}} \right)R_{2}} + {\left( {\sum\limits_{l = 0}^{389}{h_{l}h_{l + 130}}} \right)S_{3}} + {\left( {\sum\limits_{l = 0}^{324}{h_{l}h_{l + 195}}} \right)S_{4}} +}\quad} \\{\quad {{\left( {\sum\limits_{l = 0}^{259}{h_{l}h_{l + 260}}} \right)S_{5}} + {\left( {\sum\limits_{l = 0}^{194}{h_{l}h_{l + 325}}} \right)S_{6}} + {\left( {\sum\limits_{l = 0}^{129}{h_{l}h_{l + 390}}} \right)S_{7}} + {\left( {\sum\limits_{l = 0}^{64}{h_{l}h_{l + 455}}} \right)S_{8 = 0}}}}\end{matrix}{and}} & {{Eq}.\quad 28} \\\begin{matrix}{\quad {{\left( {\sum\limits_{l = 0}^{454}{h_{l}h_{l + 65}}} \right)R_{1}} + {\left( {\sum\limits_{l = 0}^{454}h_{l}^{2}} \right)R_{2}} + {\left( {\sum\limits_{l = 0}^{389}{h_{l}h_{l + 65}}} \right)S_{3}} + {\left( {\sum\limits_{l = 0}^{324}{h_{l}h_{l + 130}}} \right)S_{4}} +}} \\{\quad {{{\left( {\sum\limits_{l = 0}^{259}{h_{l}h_{l + 195}}} \right)S_{5}} + {\left( {\sum\limits_{l = 0}^{194}{h_{l}h_{l + 260}}} \right)S_{6}} + {\left( {\sum\limits_{l = 0}^{129}{h_{l}h_{l + 325}}} \right)S_{7}} + {\left( {\sum\limits_{l = 0}^{64}{h_{l}h_{l + 390}}} \right)S_{8}}} = 0}}\end{matrix} & {{Eq}.\quad 29}\end{matrix}$

[0081] Which is simplified by setting a variable equal to the summationterms, and rewritten as:

α₁₁ R ₁+α₁₂ R ₂ =−c ₁₁ S ₃ −c ₁₂ S ₄ −c ₁₃ S ₅ −c ₁₄ S ₆ −c ₁₅ S ₇ −c ₁₆S ₈  Eq.30

[0082] and

α₁₂ R ₁+α₂₂ R ₂ =−c ₂₁ S ₃ −c ₂₂ S ₄ −c ₂₃ S ₅ −c ₂₄ S ₆ −c ₂₅ S ₇ −c ₂₆S ₈  Eq.31

[0083] Solving for R₁ and R₂ and converting to matrix mathematicsyields: $\begin{matrix}{\begin{bmatrix}R_{1} \\R_{2}\end{bmatrix} = {\begin{bmatrix}a_{11} & a_{12} \\a_{12} & a_{22}\end{bmatrix}^{- 1}\begin{bmatrix}{{- c_{11}}S_{3}} & {{- c_{12}}S_{4}} & {{- c_{13}}S_{5}} & {{- c_{14}}S_{6}} & {{- c_{15}}S_{7}} & {{- c_{16}}S_{8}} \\{{- c_{21}}S_{3}} & {{- c_{22}}S_{4}} & {{- c_{23}}S_{5}} & {{- c_{24}}S_{6}} & {{- c_{25}}S_{7}} & {{- c_{26}}S_{8}}\end{bmatrix}}} & {{Eq}.\quad 32}\end{matrix}$

[0084] And defining c′_(xy)=−c_(xy) we have: $\begin{matrix}{{\begin{bmatrix}R_{1} \\R_{2}\end{bmatrix} = {{\begin{bmatrix}a_{11} & a_{12} \\a_{12} & a_{22}\end{bmatrix}^{- 1}\begin{bmatrix}c_{11}^{\prime} & c_{12}^{\prime} & c_{13}^{\prime} & c_{14}^{\prime} & c_{15}^{\prime} & c_{16}^{\prime} \\c_{21}^{\prime} & c_{22}^{\prime} & c_{23}^{\prime} & c_{24}^{\prime} & c_{25}^{\prime} & c_{26}^{\prime}\end{bmatrix}}\begin{bmatrix}S_{3} \\S_{4} \\S_{5} \\S_{6} \\S_{7} \\S_{8}\end{bmatrix}}}{and}} & {{Eq}.\quad 33} \\{\begin{bmatrix}a_{11} & a_{12} \\a_{12} & a_{22}\end{bmatrix}^{- 1} = {{\frac{1}{{a_{11}a_{22}} - a_{12}^{2}}\begin{bmatrix}a_{22} & {- a_{12}} \\{- a_{12}} & a_{11}\end{bmatrix}} = \begin{bmatrix}b_{11} & b_{12} \\b_{12} & b_{22}\end{bmatrix}}} & {{Eq}.\quad 34}\end{matrix}$

[0085] Substituting b_(xy) for like elements in the a_(xy) ⁻¹ matrixproduces Equation 35 below: $\begin{bmatrix}R_{1} \\R_{2}\end{bmatrix} = {\begin{bmatrix}{{b_{11}c_{11}^{\prime}} + {b_{12}c_{21}^{\prime}}} & {{b_{11}c_{12}^{\prime}} + {b_{12}c_{22}^{\prime}}} & {{b_{11}c_{13}^{\prime}} + {b_{12}c_{23}^{\prime}}} & {{b_{11}c_{14}^{\prime}} + {b_{12}c_{24}^{\prime}}} & {{b_{11}c_{15}^{\prime}} + {b_{12}c_{25}^{\prime}}} & {{b_{11}c_{16}^{\prime}} + {b_{12}c_{26}^{\prime}}} \\{{b_{12}c_{11}^{\prime}} + {b_{22}c_{21}^{\prime}}} & {{b_{12}c_{12}^{\prime}} + {b_{22}c_{22}^{\prime}}} & {{b_{12}c_{13}^{\prime}} + {b_{22}c_{23}^{\prime}}} & {{b_{12}c_{14}^{\prime}} + {b_{22}c_{24}^{\prime}}} & {{b_{12}c_{15}^{\prime}} + {b_{22}c_{25}^{\prime}}} & {{b_{12}c_{16}^{\prime}} + {b_{22}c_{26}^{\prime}}}\end{bmatrix}\begin{bmatrix}S_{3} \\S_{4} \\S_{5} \\S_{6} \\S_{7} \\S_{8}\end{bmatrix}}$

[0086] This solution can be calculated in the conventional manner. Thus,a set of coefficients can be generated, based on the filter tapcoefficients, and stored in a look-up table for use in calculating theramp-up (and ramp-down) symbols that yield the lowest energy in thetruncated tails. Ramp down is the mirror image of ramp up, given filtersymmetry.

[0087] In operation, as each TDMA data packet is received, the first andlast six valid data packets (items 148 and 150 in FIG. 9) are processedaccording to the stored coefficients and Equation 35 to produce the bestfit ramp-up symbols (items 134 and 136 in FIG. 9) as well as the bestfit ramp-down symbols (items 140 and 138 in FIG. 9) to minimize energyin the truncated tail portion of the data packet.

[0088] The improvement is apparent upon review of FIG. 14. This figurecompares a spectrum amplitude curve for a windowed ramp 176, with rampsymbols of zero, with a spectrum amplitude curve for the preferredembodiment adaptive ramp filter 178, which does not have zero rampsymbols. The curves were prepared using MATLAB, based on the preferredembodiment filter design. The improvement in the stop band isapproximately 10 dB. This affords designers a greater guard band or theability to more efficiently utilize spectrum in systems challenged forbandwidth. Note that a properly designed window can make the farout-of-band spectrum almost any attenuation value. The trade-off ofdoing this is more near-band spectral splatter. With adaptive ramping,no nearby penalty is paid, since the ramp symbols are part of thetransmit filter at the symbol rate. Windowing further improves the farout-of-band stop band for adaptive ramping, but the effects to thenear-band are not as severe, since the spectral efficiency is better tobegin with.

[0089] Filters as described herein can be used in a variety ofapplications. For example, the filters can be used in any system thatutilizes pulse shaping filters. Digital communication systems provideone such example. Filters of the present invention could be used inwireless communications (cellular, GSM, microwave, satellite), wiredcommunications (in telephone systems, cable modems), optical systems,broadcast systems (digital television, digital radio, satellite), andothers.

[0090] Thus, the present invention has been described herein withreference to a particular embodiment for a particular application. It istherefore intended by the appended claims to cover any and all suchapplications, modifications and embodiments within the scope of thepresent invention.

[0091] Accordingly,

What is claimed is:
 1. A apparatus for reducing output energy andbandwidth of an intermittent data stream through a digital filter,comprising: a digital filter, and a controller coupled to said digitalfilter and operable to calculate at least a first ramp data field inaccordance with coefficients selected to minimize energy in a truncatedtail of the digital filter as a function of at least a first data field.2. The apparatus of claim 1, and wherein said at least a first datafield is adjacent to said ramp data field.
 3. The apparatus of claim 1,and wherein said controller is further operable to window said ramp datafield.
 4. The apparatus of claim 1, and wherein said controller isfurther operable to calculate both of a ramp-up and a ramp-down rampdata field as a function of said at least a first data field and asecond data field respectively, and wherein ramp-down coefficients arethe mirror image of said coefficients.
 5. An apparatus for generatingcoefficients to reduce the output energy and bandwidth of anintermittent signal in a digital filter, comprising: a controlleroperable to calculate the energy in at least a first truncated tail datafield as a function of at least a first ramp data field and at least afirst data field, and operable to take a partial derivative of theenergy in said at least a first truncated tail data field with respectto said at least a first ramp data field, and operable to generate anequality by setting said partial derivative equal to zero, and operableto solve said equality for said at least a first ramp data field as afunction of said at least a first data field thereby generating at leasta first coefficient.
 6. The apparatus of claim 5, and wherein saidenergy in said at least a first truncated tail data field is also afunction of the digital filter tap coefficients.
 7. A method of reducingoutput energy and bandwidth of an intermittent data stream through adigital filter, comprising the step of: calculating at least a firstramp data field in accordance with coefficients selected to minimizeenergy in a truncated tail of the digital filter as a function of atleast a first data field.
 8. The method of claim 7, and wherein said atleast a first data field is adjacent to said ramp data field.
 9. Themethod of claim 7, further comprising the step of windowing said rampdata field.
 10. The method of claim 7, and wherein said calculating stepis applied to both of a ramp-up and a ramp-down ramp data field as afunction of said at least a first data field and a second data fieldrespectively, and wherein ramp-down coefficients are the mirror image ofsaid coefficients.
 11. A method generating coefficients for reducing theoutput energy and bandwidth of an intermittent signal in a digitalfilter, comprising the steps of: calculating the energy in at least afirst truncated tail data field as a function of at least a first rampdata field variable and at least a first data field variable; taking apartial derivative of the energy in said at least a first truncated taildata field with respect to said at least a first ramp data fieldvariable; writing an equality by setting said partial derivative equalto zero, and solving said equality for said at least a first ramp datafield variable as a function of said at least a first data field therebygenerating at least a first coefficient.
 12. The method of claim 11, andwherein said energy in said at least a first truncated tail data fieldis also a function of the digital filter tap coefficients.